The Galaxy poll, commissioned by Parents and Friends of Lesbians and Gays (PFLAG), also found 73% of respondents would prefer a free vote in the parliament on same-sex marriage over a national plebiscite.

The poll surveyed 1,000 people across Australia from May 25 to May 28 and coincides with a furore over Australian tennis legend Margaret Court, who announced last week via a letter to The West Australian newspaper that she would boycott Qantas over its support of same-sex marriage.

The Galaxy poll asked respondents: "If same-sex marriage is not addressed within this term of government, would you be more, or less likely to support a change of government to one that commits to a free vote directly after the next election?"

Half of all respondents said it would make no difference to their vote.

Forty percent said it would make them more likely to vote out the Turnbull government. This 40% included 26% of Coalition voters, 55% of Labor voters and 60% of Greens voters.

One in ten respondents said inaction on same-sex marriage would make them less likely to vote out the government.

Same-sex marriage is at a political impasse in Australia, where there is majority support among both the public and parliamentarians, but disagreement on how marriage reform should be dealt with.

The poll found just under three quarters of all respondents would prefer a free parliamentary vote on the issue, as opposed to 27% who would prefer to wait for a national plebiscite.

A national vote on marriage before any change is made to the Marriage Act remains the government's policy, and was included as a potential fiscal risk of $170 million in the May Budget.

The Labor opposition, the Greens Party and some crossbenchers oppose a national vote, arguing the issue should be dealt with via a parliamentary vote.

National spokesperson for PFLAG Shelley Argent said the poll showed prime minister Malcolm Turnbull's government will be turfed out at the next election if it continues to delay a vote on same-sex marriage.

"Mr Turnbull doesn't seem to understand voters are tired of the political games relating to marriage equality," she said.

Spokesperson for LGBTI rights group just.equal Rodney Croome called on same-sex marriage supporters within the Coalition to push for a free vote in the party room or cross the floor.

In March, Liberal backbencher Trent Zimmerman told ABC radio: "My personal and strong view is that it’s time for us to look at a free vote".

In February, Liberal backbencher John Alexander also told ABC radio the Coalition should take another look at holding a free vote.

Earlier this week Liberal backbencher Tim Wilson said on Sky News that the Margaret Court saga is "national silliness" prompted by the fact parliament won't resolve the issue of same-sex marriage.

"I think a lot of what's happening at the moment is people are expressing their frustration in other ways because the issue isn't being resolved," he said.

Lane Sainty is a reporter for BuzzFeed News and is based in Sydney, Australia.